The grades on a chemistry midterm at Santa Rita are normally distributed with $\mu = 75$ and $\sigma = 2.0$. Luis earned a $78$ on the exam. Find the z-score for Luis's exam grade. Round to two decimal places.
Answer: A z-score is defined as the number of standard deviations a specific point is away from the mean We can calculate the z-score for Luis's exam grade by subtracting the mean $(\mu)$ from his grade and then dividing by the standard deviation $(\sigma)$ $ { z = \dfrac{x - {\mu}}{{\sigma}}} $ $ { z = \dfrac{78 - {75}}{{2.0}}} $ ${ z \approx 1.50}$ The z-score is $1.50$. In other words, Luis's score was $1.50$ standard deviations above the mean.